Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a $0.95$ probability that he will hit it. One day, Samir decides to attempt to hit $10$ such targets in a row. Assuming that Samir is equally likely to hit each of the $10$ targets, what is the probability that he will miss at least one of them? Round your answer to the nearest tenth. $P(\text{at least one miss})=$
Solution: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (he misses at least one target) by calculating the probability of its complement (he hits every target) and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one miss})=1-P(\text{hit all }10)$ Calculations $\begin{aligned} P(\text{at least one miss})&=1-P(\text{hit all }10) \\ \\ &=1-(0.95)^{10} \\ \\ &\approx 1-0.599 \\ \\ &\approx 0.401\end{aligned}$ Answer $P(\text{at least one miss}) \approx 0.4$